### Abstract

Papadimitriou's approximation approach to the Euclidean shortest path (ESP) problem in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. Unfortunately, there are non-trivial gaps in the original description. Besides giving a complete treatment, we also give an alternative to his subdivision method which has some nice properties. Among the tools needed are root-separation bounds and non-trivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Editors | Anon |

Publisher | Publ by ACM |

Pages | 41-48 |

Number of pages | 8 |

ISBN (Print) | 0897916484 |

State | Published - 1994 |

Event | Proceedings of the 10th Annual Symposium on Computational Geometry - Stony Brook, NY, USA Duration: Jun 6 1994 → Jun 8 1994 |

### Other

Other | Proceedings of the 10th Annual Symposium on Computational Geometry |
---|---|

City | Stony Brook, NY, USA |

Period | 6/6/94 → 6/8/94 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Geometry and Topology

### Cite this

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 41-48). Publ by ACM.

**Approximate Euclidean shortest path in 3-space.** / Choi, Joonsoo; Sellen, Jurgen; Yap, Chee.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual Symposium on Computational Geometry.*Publ by ACM, pp. 41-48, Proceedings of the 10th Annual Symposium on Computational Geometry, Stony Brook, NY, USA, 6/6/94.

}

TY - GEN

T1 - Approximate Euclidean shortest path in 3-space

AU - Choi, Joonsoo

AU - Sellen, Jurgen

AU - Yap, Chee

PY - 1994

Y1 - 1994

N2 - Papadimitriou's approximation approach to the Euclidean shortest path (ESP) problem in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. Unfortunately, there are non-trivial gaps in the original description. Besides giving a complete treatment, we also give an alternative to his subdivision method which has some nice properties. Among the tools needed are root-separation bounds and non-trivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers.

AB - Papadimitriou's approximation approach to the Euclidean shortest path (ESP) problem in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. Unfortunately, there are non-trivial gaps in the original description. Besides giving a complete treatment, we also give an alternative to his subdivision method which has some nice properties. Among the tools needed are root-separation bounds and non-trivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers.

UR - http://www.scopus.com/inward/record.url?scp=0028022432&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028022432&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0897916484

SP - 41

EP - 48

BT - Proceedings of the Annual Symposium on Computational Geometry

A2 - Anon, null

PB - Publ by ACM

ER -